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The hypothesis of a real Cabibbo-Kobayashi-Maskawa matrix has been considered and found to be disfavoured by present measurements even when neglecting results from CP violation in neutral Kaon decay. The Best Linear Unbiased Estimator has…
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
A recent approach to the Beck-Fiala conjecture, a fundamental problem in combinatorics, has been to understand when random integer matrices have constant discrepancy. We give a complete answer to this question for two natural models:…
In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the…
We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension $3$ and higher and for coefficients having a finite range of dependence, we prove a pointwise version of…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
Rounding linear programs using techniques from discrepancy is a recent approach that has been very successful in certain settings. However this method also has some limitations when compared to approaches such as randomized and iterative…
We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation strategies of different degrees of nonlinearity: sparse…
Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems,…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…
We establish a sharp upper estimate for the order of a canonical system in terms of the Hamiltonian. This upper estimate becomes an equality in the case of Krein strings. As an application we prove a conjecture of Valent about the order of…
We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…
In this work, we define the notions of Wronskian and simplified Wronskian for Stieltjes derivatives and study some of their properties in a similar manner to the context of time scales or the usual derivative. Later, we use these tools to…
We first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case,…
We identified a set of four rephasing invariant parameters of the CKM matrix. They are found to exhibit hierarchies in powers of $\lambda^2$, from $\lambda^2$ to $\lambda^8$. It is shown that, at the present level of accuracy, only the…